Áireamhán Dóchúlachta Dénomhain

Faigh an dóchúlacht go n-éireoidh le k triail i n triail neamhspleách.

P( X = k) —

P( X ≤ k) —

P( X ≥ k) —

Meán (n· p) —

Difríocht —

Diall caighdeánach —

Torthaí a nuashonrú mar a chlóscríobh tú.

Maidir leis an áireamhán seo

the binomial distribution is used to calculate the number of successes in a fixed number of independent trials, each with the same success probability — the classic "how many heads in ten coin flips" problem. It returns the probability of exactly k successes, P(X = k) = C(n, k)·pᵏ·(1 − p)ⁿ⁻ᵏ), along with the cumulative probabilities of at most k and at least k successes. It also reports the distribution’s mean (n·p), variance (n·p·(1 − p)) and standard deviation, and shows the full probability distribution as a table and a chart.The binomial probability calculator uses the binomial distribution to model the number of successes in aWorked exampleWorked example: for n = 10 flips of a fair coin (p = 50%) the chance of exactly k = 3 heads is C(n, k) × 0.5³ × 0.5⁷ ≈ 11.7%. The full probability distribution is:TheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked

Ceisteanna Coitianta

Cén uair is féidir liom an dáileadh dénominal a úsáid?

Bain úsáid as é nuair a bhíonn líon seasta de thrialacha neamhspleácha ann, tá dhá thoradh ag gach triail (rath nó teip), agus is é an dóchúlacht rath mar an gcéanna gach uair - cosúil le bonn a chasadh 10 n-uaire nó míreanna lochtacha a chomhaireamh i mbaisc.

Cad é an difríocht idir P(X = k) agus P(X ≤ k)?

Is é P(X = k) an dóchúlacht go n-éireoidh le go díreach k duine, agus cuireann P(X ≤ k) suas an dóchúlacht go n-éireoidh le 0, 1,... suas go dtí k duine.

Cad é "n roghnaigh k"?

Is é C(n, k), a léitear mar "n roghnaigh k", an líon bealaí éagsúla chun a roghnú cé acu k de na n trialacha is rathúil. I gcás 10 triail agus 3 rath, tá C(10, 3) = 120 comhcheangal den sórt sin, agus cuireann gach ceann acu leis an dóchúlacht iomlán.

Cad iad meán agus diall caighdeánach dáileadh dénártha?

Is é an meán (líon na n-éachtaí a bhfuiltear ag súil leo) ná n·p agus is é an t-éagsúlacht ná n·p·(1 − p), mar sin is é an diall caighdeánach √(n·p·(1 − p)).I gcás 10 n-éagsúlachta coinín cothroma is é an meán 5 agus is é an diall caighdeánach thart ar 1.58.

Cén uair is féidir liom an dénártha a chomhtharlú le gnáthdháileadh?

Nuair a bhíonn n mór agus nuair a bhíonn n·p agus n·(1 − p) thart ar 10 ar a laghad, is féidir an dénomination a choibhneasú go maith le gnáthdháileadh leis an meán agus an diall caighdeánach céanna, agus is é sin an bunús le go leor tástálacha comhréireachta samplaí móra.

Conas a fhaigheann mé an dóchúlacht go n-éireoidh k ar a laghad?

Suimeálann P(X ≥ k) na dóchúlachta go n-éireoidh le k, k+1,... suas go n. Is ionann é agus 1 − P(X ≤ k − 1), agus tuairiscíonn an t-áireamhán dóchúlachta dénomómach seo é díreach in aice leis an luach "ar a mhéad".

API — úsáid an áireamhán seo ó chód

Glaoigh ar an áireamhán seo mar chríochphointe JSON saor in aisce - níl aon eochair ag teastáil. Seol na luachanna réimse thíos mar pharaiméadair cheist nó JSON. Léigh an doiciméadú iomlán API →

Deireadhphointe

GET https://calculator.free/api/v1/binomial-probability/

curl

curl "https://calculator.free/api/v1/binomial-probability/?n=10&k=3&p=50"

JavaScript `fetch()`

const r = await fetch(
  "https://calculator.free/api/v1/binomial-probability/?" + new URLSearchParams({
    "n": "10",
    "k": "3",
    "p": "50"
  }));
const data = await r.json();
console.log(data.results);

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Ceisteanna Coitianta

Áireamháin ghaolmhara

Deireadhphointe

curl

JavaScript fetch()

JavaScript `fetch()`